To export the libOOUIDialog gadget, click on "Download" button, save the downloaded file, go to Special:Import on the destination wiki and upload it. Then add the following to MediaWiki:Gadgets-definition page:
* libOOUIDialog[ResourceLoader|type=general|dependencies=oojs-ui,oojs-ui-widgets,oojs-ui.styles.indicators,oojs-ui.styles.icons-alerts,ext.gadget.libPolyfill|rights=hidden|hidden|default]|libOOUIDialog.js
You must have appropriate permissions on the destination wiki (including the right to edit system messages) and import from file uploads must be enabled.